Description Usage Arguments Details Value Author(s) References See Also Examples

Creates an instance of the Diggle-Gratton pairwise interaction point process model, which can then be fitted to point pattern data.

1 | ```
DiggleGratton(delta=NA, rho)
``` |

`delta` |
lower threshold |

`rho` |
upper threshold |

Diggle and Gratton (1984, pages 208-210)
introduced the pairwise interaction point
process with pair potential *h(t)* of the form

*
h(t) = ((t - δ)/(ρ - δ))^κ, { } δ ≤ t ≤ ρ
*

with *h(t) = 0* for *t < δ*
and *h(t) = 1* for *t > ρ*.
Here *δ*, *ρ* and *κ*
are parameters.

Note that we use the symbol *κ*
where Diggle and Gratton (1984) and Diggle, Gates and Stibbard (1987)
use *β*, since in spatstat we reserve the symbol
*β* for an intensity parameter.

The parameters must all be nonnegative,
and must satisfy *δ ≤ ρ*.

The potential is inhibitory, i.e.\ this model is only appropriate for
regular point patterns. The strength of inhibition increases with
*κ*. For *κ=0* the model is
a hard core process with hard core radius *δ*.
For *κ=Inf* the model is a hard core
process with hard core radius *ρ*.

The irregular parameters
*δ, ρ* must be given in the call to
`DiggleGratton`

, while the
regular parameter *κ* will be estimated.

If the lower threshold `delta`

is missing or `NA`

,
it will be estimated from the data when `ppm`

is called.
The estimated value of `delta`

is the minimum nearest neighbour distance
multiplied by *n/(n+1)*, where *n* is the
number of data points.

An object of class `"interact"`

describing the interpoint interaction
structure of a point process.

Diggle, P.J., Gates, D.J. and Stibbard, A. (1987)
A nonparametric estimator for pairwise-interaction point processes.
*Biometrika* **74**, 763 – 770.

Diggle, P.J. and Gratton, R.J. (1984)
Monte Carlo methods of inference for implicit statistical models.
*Journal of the Royal Statistical Society, series B*
**46**, 193 – 212.

1 | ```
ppm(cells ~1, DiggleGratton(0.05, 0.1))
``` |

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